I tried this, but it didn't work.
I didn't see this happen when I caught the fish. I saw character unhook the fish and put it away. But he didn't hold it in his arms. It was just in my inventory.
Maybe it's bugged. I will try again from the start. thank you for the replies!
EDIT: For anyone else who might run into this problem, I had the infinite fishing lure attached when the quest would not progress. After removing it, it worked just fine as SandraSolace said it would.